Labour Economics 5 Ž1998. 135–166
Male labor supply estimates and the decision to
moonlight
Karen Smith Conway a , Jean Kimmel
a
b
b,)
Department of Economics, Mc Connell Hall, UniÕersity of New Hampshire, Durham, NH 03824, USA
W.E. Upjohn Institute for Employment Research, 300 S. Westnedge AÕe., Kalamazoo, MI 49007, USA
Received 24 June 1994; accepted 17 April 1997
Abstract
This research improves the manner in which moonlighting is examined by recognizing
that workers may moonlight due to primary job hours constraints or because jobs are
heterogeneous. Our theoretical model permits both motives for moonlighting and considers
moonlighting in tandem with labor supply behavior on the primary job. Both primary and
secondary job hours equations are estimated using data from the SIPP for prime-aged men.
We conclude that the moonlighting decision is quite responsive to wage changes on both
jobs and arises from both motives, and that properly modeling moonlighting produces a
relatively high primary job labor supply elasticity. q 1998 Elsevier Science B.V. All rights
reserved.
JEL classification: J2; J6
Keywords: Moonlighting; Constraints; Labor supply elasticities
1. Introduction
Two labor supply issues that have received substantial attention are the
responsiveness of labor supply to wage changes and the existence of labor supply
constraints. Adjusting hours worked on a second job may be the practical and
)
Corresponding author.
[email protected].
Tel.:
q 1-616-3435541;
fax:
q 1-616-3433308;
0927-5371r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.
PII S 0 9 2 7 - 5 3 7 1 Ž 9 7 . 0 0 0 2 3 - 7
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136
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
perhaps only available response to either event; yet, most labor supply studies only
examine behavior on the primary job. Examining the motives for moonlighting
provides evidence on both the wage-responsiveness of labor supply in general and
the existence and consequences of labor supply constraints. If, for instance,
workers moonlight only when constrained on their primary jobs, then moonlighting itself implies that labor supply constraints exist and so supports the previous
literature that incorporates these constraints Že.g. Ham, 1982, 1986.. Regardless of
the motive for moonlighting, allowing for potential labor supply adjustments on
more than one job may alter the much-accepted conclusion regarding the inelasticity of male labor supply Žfor surveys, see Killingsworth, 1983; Pencavel, 1986..
By ignoring moonlighting behavior, researchers may be eliminating the most
significant avenue for short term labor supply adjustments. Our research improves
substantially the manner in which moonlighting is examined, and in so doing
sheds new light on male labor supply elasticities.
Why do some people choose to moonlight? The predominant view is that it
results from a constraint on hours worked on the primary job ŽShishko and
Rostker, 1976; O’Connell, 1979; Krishnan, 1990. 1. Due to workweek restrictions,
economic conditions or other institutional factors, the worker is unable to work Žor
earn. as much as he or she desires on the primary job ŽPJ., and thus may consider
taking a second job ŽSJ.. The decision to moonlight hinges on a comparison
between the reservation wage and the wage earned on the SJ. The reservation
wage and, therefore, the decision to moonlight will depend in part on the number
of hours worked on the PJ. A major shortcoming of the aforementioned studies is
the inclusion of Žexogenous. primary job hours in moonlighting equations estimated for all workers Ževen non-moonlighters., many of whom may be unconstrained on their primary jobs. Indeed, estimating hours worked on the PJ as a
choice variable is the purpose of a great many labor supply studies. To treat it as
fixed and exogenous for all workers is inconsistent with basic economic theory
and likely will lead to biased parameter estimates. Our econometric model corrects
this misspecification and predicts which workers are constrained on their primary
jobs.
Another explanation for moonlighting behavior is that labor supplied to different jobs may not be perfect substitutes or, put differently, the wage paid and utility
lost from the foregone leisure may not completely reflect the benefits and costs to
working. For example, working on the primary job may provide the worker with
the credentials to take on a higher paying second job, such as a university
professor who engages in consulting. Or, working on the second job may provide
1
In related studies, Paxson and Sicherman Ž1996. explore moonlighting and changing jobs as
alternative avenues for adjusting short-run labor supply, and Abdukadir Ž1992. examines the possibility
that moonlighting is caused by short-term liquidity constraints.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
137
some pleasure Žor less displeasure. but pay less than the primary job, such as a
musician who has a ‘regular’ job by day and performs at night 2 . In either
example, the costs and benefits of both jobs are more complex than the monetary
wages paid and the foregone value of leisure. When faced with such nonpecuniary
benefits and costs, optimizing behavior may lead a worker to take two jobs.
Whereas Shishko and Rostker Ž1976. and others acknowledge that such a motive
may exist, only Lilja Ž1991. explores it theoretically and empirically 3. Using
Finnish data, the author finds evidence that this second motive better explains
male moonlighting behavior than the first, more popular view. We build on Lilja’s
work by constructing a more consistent theoretical model and by modeling
explicitly the behavior on the first job.
Our research examines moonlighting behavior recognizing that workers may
moonlight because of constraints on their primary jobs or because the two jobs are
heterogeneous. Specifically, we devise a theoretical model that permits these
different reasons for moonlighting and considers moonlighting in tandem with
labor supply behavior on the primary job. We then estimate both primary and
secondary job hours equations using data from the SIPP Žsurvey of income and
program participation. for prime-aged men. Recognizing that most other data
sources do not contain the information necessary to model fully moonlighting
behavior, we also estimate several simpler models of primary labor supply that
deal with moonlighters in less sophisticated ways Že.g. omitting them from the
sample.. These estimates provide guidance in how to best deal with moonlighters
when second job information is incomplete or of suspect quality. More generally,
we find evidence that the decision to moonlight is quite responsive to wage
changes Žon both jobs. and arises from both motives. Properly modeling primary
job hours constraints and differences in moonlighting motives reveals that the
desired labor supply of prime-aged males is much more wage-elastic than typically
assumed.
2. A theoretical framework for multiple job-holding
We assume that a person’s labor supply decisions on the first and second job
result from utility-maximizing behavior. However, to allow for the possibility that
labor supplied to different jobs may not be equivalent, hours of work on the first
2
Still another possibility is that certain types of job situations present greater opportunities for tax
evasion. Plewes and Stinson Ž1991. provide survey evidence Žfrom the 1989 CPS. of the many distinct
reasons for moonlighting reported by workers.
3
Regets Ž1991. investigates a closely related issue, whether serving in the military reserves is
moonlighting in the usual sense or is instead a case of compensated leisure.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
138
job, h1 , hours of work on the second job, h 2 , and hours of leisure, L, enter the
utility function separately. Total utility may be written as
Utilitys U Ž C, h1 , h 2 , L . ,
Ž 1.
where C denotes consumption. If working on either job provides no Ždis.utility
beyond that caused by foregoing leisure then Eq. Ž1. simplifies to the standard
leisurerconsumption utility function. The utility function written in Eq. Ž1. is
maximized subject to both a budget and a time constraint, or
C s w 1 h1 q w 2 h 2 q Y ,
Ž 2.
T s h1 q h 2 q L,
Ž 3.
and
in addition to the usual non-negativity constraints on h i , L and C. wi denotes the
wage received for one hour worked on job i, Y is non-wage income and T is the
total amount of time available. Substituting these constraints into the utility
function for C and L yields the utility-maximizing problem,
max U Ž w 1 h1 q w 2 h 2 q Y , h1 , h 2 , T y h1 y h 2 . .
h1 , h 2
Ž 4.
We can use the utility-maximizing problem written in Eq. Ž4. to describe both
types of moonlighting behavior.
2.1. Moonlighting caused by labor supply constraints
If the worker is constrained on the primary job, then h1 is no longer a choice
variable and the only avenue for working more hours is to take a second job. This
situation is considered by Shishko and Rostker Ž1976., O’Connell Ž1979. and
Krishnan Ž1990. and is depicted in Figs. 1 and 2. Here the worker cannot work
any more than H1 hours on the PJ, and the decision to take a SJ depends on
Fig. 1. A constrained moonlighter.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
139
Fig. 2. A constrained non-moonlighter.
whether the wage paid on the SJ exceeds its marginal disutility, given that H1
hours have already been committed to the first job. Fig. 1 depicts an individual
who chooses to supply h 2 hours to a second job, whereas the worker shown in
Fig. 2 will not choose to moonlight.
Shishko and Rostker Ž1976. rigorously derive the testable implications for the
resulting moonlighting equation and so we will not repeat them here. Substituting
the constraint h1 s H1 into the problem written in Eq. Ž4. yields
max U w1 H1 q w 2 h 2 q Y , H1 , h 2 , T y H1 y h 2 ,
h2
ž
/
Ž 5.
and results in the optimizing relationship,
Ž U2 y UL . rUc s yw 2 ,
Ž 6.
where U2 denotes the partial derivative of utility with respect to h 2 . Recognizing
ŽU2 y UL . as the marginal disutility from an hour of work on the second job Žany
Ždis.utility from working minus the utility lost from the foregone leisure. reveals
that Eq. Ž6. is the familiar condition between the reservation wage and the market
wage.
Solving for hours supplied on the second job leads to the moonlighting
equation,
h 2 s h c2 Ž w 2 , Y q Ž w1 y w 2 . H1 , H1 . ,
Ž 7.
where Y q Ž w 1 y w 2 . H1 can be seen from Figs. 1 and 2 to be the ‘linearized’
intercept of the new segment of the budget line, akin to the concept of virtual
income in the income tax literature Že.g. Killingsworth, 1983.. The superscript c
identifies this function as the moonlighting function of workers who are constrained on their primary jobs. Economic theory suggests that if leisure is a normal
good then E hc2rE V - 0 where V is the virtual income measure, E hc2rE H1 - 0, and
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K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
that E hc2rE w 2 has the usual ambiguous sign. In addition, when h c2 is specified as a
linear labor supply equation, then E h c2rE H1 s y1.0 4 .
Shishko and Rostker Ž1976., O’Connell Ž1979. and Krishnan Ž1990. estimate
tobit Žor probit. moonlighting functions similar to that written in Eq. Ž7. using data
on all workers and including hours worked on the primary job as a regressor.
Hours on the primary job is a valid regressor only if it is truly fixed and
exogenous for all observations, which suggests that all workers are constrained on
their primary jobs. This is quite a heroic assumption and one that Shishko and
Rostker Ž1976. acknowledge Žsee footnote 14 on p. 304.. There is no reason to
believe that all non-moonlighters are constrained on their primary jobs, and even
moonlighters are not necessarily constrained. To assume that hours supplied to the
primary job is exogenous is to question the importance of much labor supply
research. We develop a more theoretically consistent model by estimating the
upper bound faced by workers Ž H1 . and including it in the moonlighting equation.
2.2. Moonlighting caused by heterogeneous jobs
If the first and second jobs have different nonpecuniary benefits or costs, we
may observe moonlighting among workers who are not constrained on their
primary jobs. Rather, utility-maximizing behavior leads them to supply their labor
to two different jobs. The consumer’s problem written in Eq. Ž4. once again yields
the optimizing conditions,
Ž Ui y UL . rUc s ywi , for i s 1, 2.
Ž 8.
Eq. Ž8. suggests that the individual will supply hours on job i until the marginal
disutility of working another hour Ždivided by the marginal utility of income. is
just equal to the Žnegative. wage paid on the job. Clearly, rational behavior will
lead to moonlighting only if there are nonpecuniary benefits or costs to working
on job i, represented by Ui above. For instance, if the two jobs are identical and
impose no additional costs or benefits beyond the utility lost to the foregone
leisure, Eq. Ž8. simplifies to
yULrUc s ywi ,
for i s 1, 2,
Ž 9.
and the worker should supply all of his or her labor to the job paying the highest
hourly wage.
4
This can be seen by reviewing Fig. 1 and noting that an alternative way of estimating the
individual’s labor supply would be to estimate total hours Žor H1 q h 2 . as a function of w 2 and virtual
income. ŽAgain, this is similar to estimating labor supply in the presence of progressive income
taxation after ‘linearizing’ the budget line.. Therefore, if we estimate only h 2 as a function of w 2 ,
virtual income, and H1 then the partial derivative E h 2 rE H1 Žor coefficient on H1 with a linear labor
supply equation. equals y1.0.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
141
If jobs are indeed heterogeneous, then we observe two labor supply equations
of the form
h i s hui Ž w1 , w 2 , Y . ,
for i s 1, 2,
Ž 10.
where hui denotes an unconstrained labor supply Žand moonlighting, for i s 2.
function. Comparative statics for such a model Žavailable upon request., given
standard assumptions about the utility function, suggest that E h irE wj - 0 for i / j,
with the usual ambiguous sign when i s j. Assuming that leisure is a normal good
suggests E h irE Y - 0. The reader may recognize this problem as being similar to
the one facing the individual who can supply labor to either household or market
production activities; therefore, the same theoretical results apply Žsee Gronau,
1973..
Permitting two alternative motives suggests that there are two different moonlighting functions, one for those workers who moonlight in response to a labor
supply constraint on the primary job Žwritten in Eq. Ž7.. and another for those who
moonlight because the two jobs have differences that go beyond the monetary
wage paid Žwritten in Eq. Ž10... As mentioned earlier, Lilja Ž1991. is the first to
explore explicitly both motives for moonlighting and to implement the resulting
different functions, correcting for the simultaneity bias resulting when one includes hours worked on the primary job as a determinant of h c2 . However, the
paper has several shortcomings. First, Lilja specifies an inappropriate utility
function to study the issue; most importantly, Lilja assumes the utility function is
separable in hours worked on the first and second jobs and fails to recognize that
they must at least be linked through the time constraint 5. Thus, the resulting
unconstrained moonlighting equation is only a function of w 2 and Y, and excludes
the primary job wage. Hours worked on the primary job also fails to appear in the
constrained moonlighting equation except as part of non-wage Žor virtual. income.
Second, while using an instrument for H1 Žthe predicted value of hours worked on
the primary job as a function of all exogenous variables in the system., Lilja fails
to model it as a labor supply constraint that should be a function of labor demand
variables only. Finally, the models he estimates and the tests performed on them
require that all workers fit just one of the two profiles — i.e. all must moonlight
for the same reason.
2.3. Some testable implications
Our research addresses the above described shortcomings by building a consistent theoretical and empirical model that jointly explains labor supply behavior on
5
Specifically, Lilja Ž1991. specifies a Cobb–Douglas utility function in C, h1 and h 2 that is
maximized subject to the budget constraint only. Therefore the value of leisure, the essential link
between the two jobs, in no way enters into the analysis.
142
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
both jobs and provides testable hypotheses. We accomplish this by explicitly
modeling the behavior of the four possible types of workers, described by the cell
diagram Table 1.
It is illuminating to consider the different predicted behaviors of these four
groups and to consider some special cases. Consider first the two kinds of
moonlighters Žgroups I and II.. We would expect group I to moonlight for longer
periods of time, with no particular relationship between the wages paid on the two
jobs. Conversely, group II moonlights in response to labor supply constraints on
the first job and therefore would be expected to moonlight only temporarily. ŽIn
the long run, we would expect them to find a primary job that matches more
closely their desired hours of work. See, for example, Altonji and Paxson Ž1988...
Also, the wage on the second job will not be greater than that on the primary job if
the two jobs are otherwise identical. In general, then, we would expect to see
shorter, more sporadic episodes of moonlighting on lower paying jobs if the labor
supply constraint motive is important, and observe more prolonged episodes of
moonlighting with no particular relationship between the PJ and SJ wages if the
heterogeneous jobs motive is present Žsee Kimmel and Smith Conway Ž1996...
Two special cases are also worth noting. Shishko and Rostker Ž1976., O’Connell Ž1979. and Krishnan Ž1990. all assume that only two groups of workers,
groups II and IV, exist. In other words, they assume that all workers are
constrained on their primary jobs; thus, one is justified in including hours worked
on the primary job as a regressor in the moonlighting equation. Our theoretical
framework emphasizes the inappropriateness of this assumption and suggests a test
of its validity. Specifically, we perform a Hausman exogeneity test by using two
different measures of H1 Žobserved PJ hours and the predicted upper bound H1 .
for all regressors that are constructed using primary job hours information and
then test the equality of their coefficients. If we fail to reject exogeneity then this
seemingly inappropriate assumption is supported by the data.
Another special case is if only groups II and III exist, or if all moonlighters are
constrained on their primary jobs and all non-moonlighters are unconstrained. As
pointed out by Shishko and Rostker Ž1976, footnote 8, p. 302., one labor supply
equation could then be estimated for all workers, in which total hours worked
Ž h1 q h 2 . is a function of the marginal wage Ž w 1 for non-moonlighters, w 2 for
moonlighters. and the linearized intercept of the budget line Žeither Y or Y q Ž w1
Table 1
On primary job
Moonlighters
Non-moonlighters
unconstrained
constrained
I: h1 ; hu2 ) 0
III: h1; hu2 s 0
II: H1; hc2 ) 0
IV: H1; hc2 s 0
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
143
y w 2 . H1 , respectively.. However, to permit the behavior exhibited by all four
groups, we must also explicitly model labor supply behavior on the primary job.
3. Econometric specification
3.1. Hours worked on the primary job
The above discussion reveals the importance of knowing whether workers are
constrained in modeling both their PJ and SJ labor supply. Some surveys, such as
the PSID, ask the respondent if he or she was able to work as much Žor little. as
desired on the primary job. One could then use such information to construct a
separation indicator that sorts the observations into one regime or another,
although evidence exists that the survey questions may yield ‘noisy’ or imperfect
sample separation information ŽDouglas et al., 1995..
Unfortunately, the SIPP data do not contain such survey information. We
therefore have no separation indicator available and must treat it as unknown.
Instead, we estimate who is constrained on their PJ via a disequilibrium model of
labor supply and demand. While intuitive, this method relies heavily on assumed
differences between variables explaining labor supply versus labor demand and on
parametric assumptions Žthe assumed bivariate normal distribution of the errors.. It
may also be sensitive to model specification, a possibility that we explore. In sum,
while it is desirable to have Žpossibly noisy. separation indicator data, we believe
that the advantages of the SIPP, such as its ability to identify if two jobs were
actually held simultaneously and to track short-term job movements, outweigh this
shortcoming.
In our disequilibrium model, the hours worked on the primary job is the
minimum of desired labor supply and the upper bound on hours worked, H1 6 . In
particular, observed hours of work on the primary job, h1 , is generated by
h1s s X sb s q e s ,
where e s i.i.d. N Ž 0, ss 2 . ,
h1d s X db d q e d ,
where e d i.i.d. N Ž 0, sd2 . , and,
h1 s min Ž
h1s ,
h1d
.,
s
d
Corr Ž e , e . s r , and
Ž 11 .
h1d ' H1 .
The disequilibrium model written in Eq. Ž11. is similar to the one pioneered by
Fair and Jaffee Ž1972. and discussed further by Quandt and Ramsey Ž1978. and
6
Note that our framework ignores the possibility that a worker may be overemployed and that H1
may be a lower bound as well. Although this is an unfortunate limitation, we can take comfort in the
fact that most survey evidence Žsuch as that from the PSID. finds overemployment to be far less
prevalent than underemployment and that overemployment should not lead to moonlighting behavior.
An interesting application of a disequilibrium model to the problem of overemployment, or a lower
bound on hours worked, is Moffitt Ž1982..
144
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
Kiefer Ž1980., in which there is exogenous switching between two regimes
Ždenoted here as s or d. based on either an observed or unobserved separation
indicator 7.
The variables in the desired labor supply equation are implied by Eq. Ž10. and
include the wages on the primary and second jobs, non-wage income and a vector
of taste variables such as education, age, number of children, marital status and
health status. The variables in the labor demand equation include the wage on the
PJ, education, industry and occupation variables, labor market conditions Žthe state
unemployment rate and region. and time and time squared to pick up any trends in
economic conditions over time. However, note that hd is not a labor demand
equation in the usual sense; rather, it is the maximum hours an individual can
work on his primary job and is a function of his skills, job characteristics and
economic conditions 8.
Estimating the model written in Eq. Ž11., treating the separation indicator as
unknown, yields several useful results. First, we can examine the signs of
E h1s rE w 2 and E h1s rE w1. If moonlighting arises from heterogeneous jobs then
E h1s rE w 2 should be negative; otherwise, it should be zero. Also, if E h1s rE w 2 is
statistically important and the wages on the primary and secondary jobs are
positively correlated Žas is likely., then omitting the second wage Žas most studies
do. may bias downward the estimate of E h1s rE w 1. By including w 2 , we may find
that primary labor supply is more wage-responsive than typically believed.
Estimating Eq. Ž11. also allows us to calculate both the probability that any one
worker is constrained ŽprobŽ h1s ) h1d .. and the level of that constraint, hˆ 1d or H1.
One estimate of the probability is the marginal or unconditional probability that a
worker is constrained, or probŽ h1s ) h1d . s probŽ e d y e s - X sb s y X db d .. As Kiefer
Ž1980. notes, however, a superior estimate would be one that also uses information
about the observed outcome, or probŽ h1s ) h1d < h1 ., typically referred to as the
conditional probability. Burkett Ž1981. explores empirically the difference between
the estimated conditional and marginal probabilities in disequilibrium models
where r s 0, and Lee Ž1984. proves that using the conditional probability
minimizes the total probability of misclassification. We therefore choose to use the
conditional probability in our second stage.
7
See Maddala Ž1983. and Quandt Ž1988. for surveys and further discussion of such models. For
examples of labor supply disequilibrium models see Moffitt Ž1982., Phipps Ž1991. or Quandt and
Rosen Ž1988..
8
One might argue that occupation and industry Žand even region. are choice variables over the long
run because individuals choose occupations that will likely match their long-run desired labor supply.
This suggests that, in the long run, desired labor supply should be equal to or less than the typical
maximum hours allowed on the job the person has chosen. In the short run, however, desired labor
supply may differ from the maximum hours allowed and the latter is more likely to be influenced by
occupation and industry.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
145
Examining the distribution of the Žconditional. probability of being constrained
across moonlighters and non-moonlighters provides evidence as to the relative
importance of each group of worker Žgroups I–IV, discussed above.. More
importantly, the estimated probabilities, as well as the estimated upper bound on
primary hours, H1 , are necessary to control for potential PJ constraints in the
moonlighting hours equation.
3.2. A general moonlighting function
According to our theoretical model, workers have different moonlighting
functions depending upon their motives for moonlighting. In particular, desired
hours on the second job is distributed as
f Ž h2 . s
h c2 Ž w 2 , Y q Ž w 1 y w 2 . H1 , H1 .
if hs ) hd ,
or f Ž h 2 < h1s ) h1d .
hu2 Ž w1 , w 2 , Y .
if hs F hd ,
or f Ž h 2 < h1s F h1d .
Ž 12 .
which can be written and estimated as
h 2 s h c2 Ž w 2 , Y q Ž w1 y w 2 . H1 , H1 . )Pr Ž h1s ) h1d < h1 .
q hu2 Ž w1 , w 2 , Y . )Pr Ž h1s F h1d < h1 . .
Ž 13 .
From our estimation of the hours worked on the primary job via Eq. Ž11., we
obtain estimates of H1Žs X db d . and the probability of being constrained or
unconstrained Žgiven observed PJ hours, h1 .. We include the probability of being
constrained in Eq. Ž13. rather than using it to construct a dummy variable that
classifies workers as constrained Žor not. for several reasons. Foremost, we believe
that the probability contains more information and is less arbitrary. For instance, a
worker with a probability of being constrained of 0.51 is probably more similar to
a worker with a probability of 0.49 than one with a probability of 0.99, yet this
distinction is lost with a dummy variable. Second, the two motives are not
necessarily mutually exclusive Žalthough our theoretical model assumes they are..
For instance, a worker who is suffering from hours constraints on his PJ may
decide to take a second job that he also enjoys more and perhaps shows long run
potential, such as a factory worker who moonlights as a handyman, an activity he
enjoys more and one that he hopes might lead to a permanent business. Under this
scenario, the probabilities may instead be viewed as the weight or strength of each
motive in the moonlighting behavior of the worker.
We use Eq. Ž13. to estimate both discrete and continuous moonlighting
behavior. We use the probit procedure to estimate the decision to moonlight for all
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K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
workers, then we estimate an hours equation for moonlighters only, correcting for
self-selection bias 9. We estimate the model both ways to explore the difference
between the discrete decision to moonlight and the choice of hours on the second
job, given that one has decided to moonlight.
Testable hypotheses from our estimates of Eq. Ž13. include the statistical
significance and sign of E h 2rE wi Ž i s 1, 2., and the relative importance of the
constrained versus the unconstrained moonlighting functions. We also test whether
observed hours on the primary job is exogenous by performing a Hausman
exogeneity test ŽHausman, 1978.. These results shed light on the validity of past
studies that assume all workers are constrained on their primary jobs. They also
reveal how much meaningful information about labor supply behavior is being lost
when researchers ignore or omit moonlighters from empirical labor supply studies.
A final problem remains. We do not observe the wage on the second job for
non-moonlighters and we must therefore estimate it using data for moonlighters
only, correcting for self-selection bias. The very first stage of our analysis, then, is
to estimate a reduced form moonlighting participation equation Žwhich is derived
in Appendix A and includes all of the exogenous variables in the system’s
equations. in order to construct the inverse Mills ratio. Then, for each job, we
estimate a standard Mincer-type wage equation, with controls added for local labor
market conditions and age-education interactive variables Žas suggested by Mroz,
1987. 10 . In addition, this same inverse Mills ratio is used to correct for self-selection bias in the moonlighting hours equation. Fig. 3 summarizes and clarifies the
various stages of our analysis.
4. Data and descriptive analysis
We use the 1984 survey of income and program participation ŽSIPP. panel for
our empirical analyses. In the SIPP, each household is surveyed nine times, once
every four months for 36 months. Detailed non-labor income and labor force data
are collected, with job-specific information recorded for up to two jobs at each
interview. We choose the SIPP data for our empirical analysis because it has
detailed information on the second job that is superior to that available in other
surveys Žnamely the panel study of income dynamics, national longitudinal survey,
9
An additional complication with the hours equation is that both hc2 and hu2 must be greater than or
equal to zero. Rather than impose this restriction, we instead check whether our estimates satisfy it. We
discuss this further in Section 5.
10
In particular, the wage equations include a complete quadratic in age and education and all of the
variables in the labor demand equation.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
147
Fig. 3. Outline and purpose of the different stages of estimation.
and current population survey., and it has a short Žfour month. survey period that
better measures worker movements into and out of jobs. While both the PSID and
the NLS Žnational longitudinal survey. contain annual data, the SIPP provides data
measured with greater frequency and requiring less long-term recall. The major
148
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
drawbacks of the SIPP are the limited duration of each panel, and the unavailability of tax information 11 . The latter is particularly unfortunate because the tax
function could be both a motive for moonlighting Ži.e., by encouraging greater tax
evasion; see 2 . and a factor that influences the allocation of hours between the
two jobs.
To construct the estimating sample, we impose the following theoreticallymotivated exclusion criteria. First, any individual younger than age 18 or older
than age 55 at any point in the panel was omitted. Second, any individual from the
age of 18 to 25 who was in school was excluded. The goal here was to omit those
individuals who were likely to be making concurrent labor force decisions and
human capital investment decisions. While this exclusion is certainly not random
and may cause some self-selection bias, eliminating all individuals under age 26
greatly reduces the moonlighting observations in our sample Žfrom 593 to 504.. In
fact, this selection at age 26 would result in a 15 percent drop in the number of
moonlighting observations and a 24 percent drop in the number of moonlighting
individuals. In order to bolster our sample size and make the empirical analysis
feasible, we therefore make this selective exclusion. We have also excluded the
self-employed and those in the military 12 . Finally, in order to simplify the
econometric analysis to follow, we have included only those men who held at least
one job during each wave in the panel. This results in a balanced panel Ži.e., each
individual has 9 waves of data., reducing the need to further complicate an already
sophisticated estimation technique by modeling the probability of employment in
the primary job.
Labor supplied to each job Ž h i . is defined as the total hours worked during the
wave. We identify the primary job ŽPJ. as the one that pays the higher wage. Other
definitions are possible, such as the job with the higher earnings or hours worked,
and the heterogeneous jobs motive makes any distinction between the two jobs
murky. We choose this definition because it is consistent with our theoretical
model; only for the ‘constrained’ motive is the ranking of primary and secondary
jobs truly meaningful, and according to this motive the PJ must be the job that
11
In addition, estimating tax rates for our sample would be practically and conceptually difficult
because income taxes are based on annual income. As a practical difficulty, our survey periods
sometimes contain two calendar years and necessary information such as number of dependents or the
amount of deductions are not available. Defining one’s marginal and average tax rate for January
through April, for example, is conceptually difficult both because data may be missing on the later
months and because the worker’s own assumptions about his future income Žand therefore labor
supply. are required for such a calculation.
12
While excluding the self-employed omits some moonlighters, it allows us to avoid the fundamental
problem of distinguishing returns to labor from returns to capital. This practice is consistent with
previous research on moonlighting Že.g. Krishnan, 1990, p. 363.. And, it is not possible to identify
moonlighting episodes for the self-employment job records in the SIPP.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
149
Fig. 4. Variable definitions.
pays the higher wage 13 . ŽIf the jobs are otherwise identical, the individual will
want to supply all of his labor to the higher-paying job.. The wage measure for
each job Ž wi . is the reported earnings for the job divided by the reported hours,
deflated by the consumer price index. Using this imputed wage measure will tend
to bias the wage coefficient downward ŽBorjas, 1980.. For that reason and the fact
that the SJ wage is unobserved for non-moonlighters, we estimate PJ and SJ wage
equations, in order to create predicted wage measures for use in the empirical
analysis. A detailed data description given in Appendix B outlines further the
intricacies of the SIPP data.
Our sample consists of 1,832 males, 11% of whom moonlight at some point in
the panel. This yields a sample of 593 moonlighting observations and 211
moonlighting individuals. These numbers are unfortunately small, but entirely
13
For completeness, we also estimated the model ranking the jobs according to earnings and then, in
case of a tie, by usual weekly hours worked. This change affected less than 25% of the moonlighting
observations and had little effect on the empirical results, with the understandable exception of the
moonlighting hours equation. These results are available upon request.
150
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
Table 2
Variable means Žstandard deviation in parentheses.
full sample
moonlighting
non-moonlighting
I. 0–1 Dummy variables
Sample sizes Žaindividuals.
YNGKIDS
SICK
NONWHITE
MARRY
MOONNOW
MOONEVER
NORTHEAST
SOUTH
WEST
16,488 Ž1,832.
0.26 Ž0.44.
0.04 Ž0.19.
0.10 Ž0.29.
0.76 Ž0.43.
0.04 Ž0.19.
0.11 Ž0.32.
0.23 Ž0.42.
0.31 Ž0.46.
0.18 Ž0.38.
593
0.33 Ž0.47.
0.017 Ž0.13.
0.14 Ž0.34.
0.78 Ž0.41.
1.00 Ž0.00.
1.00 Ž0.00.
0.29 Ž0.45.
0.32 Ž0.47.
0.13 Ž0.34.
15,895
0.26 Ž0.44.
0.04 Ž0.19.
0.09 Ž0.29.
0.76 Ž0.43.
—
0.08 Ž0.27.
0.22 Ž0.42.
0.31 Ž0.46.
0.18 Ž0.38.
II. Continuous variables
AGE
PJHRWAVE
PJWAGE
SJHRWAVE
SJWAGE
NONLABY
VIRTUAL Y a
NUMKIDS
YRSEDUC
UNEMPL
36.89 Ž9.22.
726.45 Ž165.25.
10.16 Ž3.23.
13.21 Ž86.42.
3.62 Ž1.71.
4189.6 Ž4850.
9127.82 Ž5348.
0.90 Ž1.11.
13.17 Ž2.80.
7.66 Ž1.81.
35.16 Ž8.56.
553.02 Ž260.62.
9.70 Ž2.97.
367.37 Ž278.72.
4.08 Ž1.70.
3736.2 Ž4356.
7983.13 Ž4753.
1.31 Ž1.24.
13.83 Ž2.72.
7.51 Ž1.74.
36.96 Ž9.24.
732.92 Ž156.94.
10.18 Ž3.23.
—
3.60 Ž1.71.
4205.5 Ž4866.
9170.52 Ž5364.
0.88 Ž1.10.
13.15 Ž2.80.
7.67 Ž1.82.
a
Constructed as a function of H1 , the predicted upper bound on primary job hours.
consistent with national evidence that only a very small percentage of workers
report holding two or more jobs at any given time. This suggests that future
research on moonlighting should perhaps conduct surveys that oversample moonlighters to obtain a larger sample 14 . See Fig. 4 for a list of the variables and their
definitions, and Table 2 for the variable means. Not reported in the tables is the
number and duration of moonlighting episodes experienced by the workers. Of the
211 people who moonlight at some point during the sample, 175 have only one
episode, 31 have two, and the remaining five have three episodes. These episodes
last only one time period Žfour months or less. for the majority of moonlighters
Ž121 out of 211.. At the other extreme, only 14 individuals moonlight all nine time
14
Another option would be to permit an unbalanced panel; however, adding those individuals who
did not work at all at some point during the panel likely would not add many observations as
moonlighters tend to be strongly attached to the labor force.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
151
periods. These descriptive statistics point to the constraint motive for moonlighting
because they reveal short-term, sporadic episodes of moonlighting.
5. Empirical results
Referring to Fig. 3, our model requires three stages of estimation — the initial
stage, the primary hours specification and the moonlighting specification. For the
initial stage, the results from the reduced form moonlighting participation equation
are not reported in the paper for the sake of brevity but are available upon request.
The primary and secondary wage equation results are given in Table 3. Empirical
results for the primary job hours equation are listed in Table 4 and the moonlightTable 3
Initial stage wage equation results Ž t-statistics in parentheses.
YRSEDUC
YRSEDUC2
AGE
AGE2
YRSEDUC)AGE
WAVE
WAVE2
UNEMPL
NONWHITE
NORTHEAST
SOUTH
WEST
PJPRTECH
PJSALES
PJCLERIC
PJSERVWK
PJLABOR
PJOCRAFT
PJOPTIV
PJICRAFT
PJMANUF
PJUTIL
PJTRADE
PJBUSSRV
PJPRSSRV
PJPRFSRV
MILLS
INTERCEPT
R-SQUARED
F-STATISTIC
)
Significant at 10 percent.
Significant at 5 percent.
))
PJ wage
SJ wage
y0.58 ) ) Žy6.43.
0.01) ) Ž5.25.
0.25 ) ) Ž7.67.
y5Ey3 ) ) Žy12.51.
0.02 ) ) Ž15.53.
y0.04 Žy0.77.
4Ey3 Ž0.73.
y0.11) ) Žy5.71.
y1.21) ) Žy10.88.
y0.14 Žy1.44.
y0.58 ) ) Žy6.73.
0.81) ) Ž8.24.
y0.60 ) ) Žy4.86.
y1.63 ) ) Žy10.91.
y2.94 ) ) Žy18.68.
y3.13 ) ) Žy19.44.
y3.78 ) ) Žy23.09.
y2.00 ) ) Žy16.36.
y3.11) ) Žy23.82.
0.84 ) ) Ž4.75.
0.84 ) ) Ž5.58.
1.48 ) ) Ž8.82.
y0.79 ) ) Žy4.76.
0.44 ) ) Ž2.53.
y1.88 ) ) Žy16.91.
y2.76 ) ) Žy16.91.
—
5.60 ) ) Ž5.46.
0.3797
387.47 ) )
y0.86 ) Žy1.87.
0.02 Ž1.42.
0.25 ) Ž1.84.
y5Ey3 ) ) Žy3.25.
0.01) ) Ž2.21.
y0.18 Žy0.86.
0.02 Ž1.19.
y0.25 ) ) Žy3.00.
y0.73 Žy1.56.
y0.14 Žy0.37.
y0.97 ) ) Žy2.82.
0.13 Ž0.28.
0.88 ) Ž1.86.
0.99 ) Ž1.81.
1.23 ) ) Ž2.07.
0.55 Ž1.12.
0.37 Ž0.52.
0.47 Ž0.85.
0.65 Ž1.10.
1.05 Ž1.19.
y1.39 ) ) Žy2.47.
y1.39 ) ) Žy2.47.
y0.83 Žy1.57.
y0.52 Žy1.04.
y1.26 Žy1.54.
0.04 Ž0.09.
y0.28 Žy0.55.
6.78 Ž1.38.
0.2490
6.938 ) )
152
Single equation
s
h variables
Switching regression
s
h coefficients
))
Ž11.02.
PJWAGE
8.02
SJWAGE
y4.34 ) ) Žy3.82.
NONLABY
y0.2Ey2 ) ) Žy4.33.
YRSEDUC
y10.36 ) ) Žy3.89.
YRSEDUC2
0.41) ) Ž3.88.
AGE
7.77 ) ) Ž5.56.
AGE2
y0.10 ) ) Žy5.60.
MARRY
26.64 ) ) Ž7.34.
YNGKIDS
11.37 ) ) Ž3.00.
NUMKIDS
y6.44 ) ) Žy4.16.
SICK
y10.73 Žy1.62.
CONSTANT
575.84 ) ) Ž19.50.
SIGMA
162.07
RHO
—
11
Goodness of fit measure F16476
s60.39 ) )
a
hs variables
PJWAGE
SJWAGE
NONLABY
YRSEDUC
YRSEDUC2
AGE
AGE2
MARRY
YNGKIDS
NUMKIDS
SICK
CONSTANT
SIGMA
RHO
hs coefficients
hd variablesa
hd coefficientsa
))
PJWAGE
UNEMPL
—
YRSEDUC
YRSEDUC2
WAVE
WAVE2
NONWHITE
—
—
—
CONSTANT
SIGMA
RHO
1.63 Ž1.25.
y2.29 ) ) Žy3.14.
—
y7.31) ) Žy2.96.
0.37 ) ) Ž3.79.
0.34 Ž0.17.
y0.06 Žy0.32.
y289.60 ) ) Žy5.58.
—
—
—
800.01) ) Ž35.08.
129.72
0.1886 Ž1.10.
Ž8.18.
76.29
y57.61) ) Žy5.43.
y0.3Ey2 Žy1.20.
y33.93 Žy1.29.
0.17 Ž0.17.
32.43 ) ) Ž2.76.
y0.37 ) ) Žy2.50.
129.25 ) ) Ž3.93.
74.86 ) ) Ž2.55.
y38.71) ) Žy3.01.
y94.85 ) Žy1.72.
746.85 ) ) Ž2.91.
524.02
0.1886 Ž1.10.
Additional hd controls: 3 regional dummies; 7 occupation dummies; 8 industry dummies.
Significant at the 10% level.
))
Significant at the 5% level.
)
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
Table 4
Results from primary job hours equation Ž t-statistics in parentheses.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
153
ing equation estimates appear in Tables 5 and 6. We also estimate both the
primary and secondary hours equations in the usual Žand, we argue, inconsistent.
way so that we can see how our more theoretically consistent specification alters
the results.
We specify the labor supply equation Žboth primary hours and moonlighting
equations. as a linear Žconstant slope. function. Although more restrictive than
some other functional forms Že.g., see Stern, 1986., it has several advantages.
Most importantly, the wage enters in only once Žas opposed to a quadratic form,
for instance.. Given that we must include both wages and that both are predicted,
having to include multiple forms of the wages greatly complicates the model. It is
also a relatively popular specification and it simplifies our interpretation of the
coefficient on H1 Žsee 4 .. Although we have panel data, we are unable to
incorporate fully unobserved individual heterogeneity. It is well beyond the scope
of this paper to develop and estimate a switching regression model that incorporates individual heterogeneity. To estimate a fixed effect probit moonlighting
equation, individuals who did not moonlight at all or who always moonlighted
Table 5
Secondary job hours equations – Probit coefficients for all workers Ž t-statistics in parentheses.
PJ hours constraineda
PJ hours not constrainedb
Full model c
A. variables in constrained equation
SJWAGE
0.03 Ž1.50.
VIRTUAL Y
y0.2Ey4 ) ) Žy4.50.
H1
y0.2Ey2 ) ) Žy3.17.
—
—
—
y0.02 Žy0.99.
y0.2Ey4 ) Žy1.67.
y0.2Ey1) ) Žy6.00.
B. variables in unconstrained equation
SJWAGE
—
NONLABY
—
PJWAGE
—
0.04 ) ) Ž2.35.
y0.8Ey7 ) Žy1.66.
y0.10 ) ) Žy9.80.
0.06 Ž1.25.
y0.2Ey4 ) ) Žy2.00.
y0.01 Žy0.45.
C. variables in all models
YNGKIDS
y0.17 ) ) Žy3.21.
NUMKIDS
0.17 ) ) Ž8.39.
AGE
y0.08 ) ) Žy3.91.
AGE2
0.9Ey3 ) ) Ž3.46.
YRSEDUC
0.05 Ž1.08.
YRSEDUC2
0.7Ey4 Ž0.04.
SICK
y0.23 ) Žy1.80.
MARRY
y0.4Ey2 Žy0.07.
CONSTANT
0.52 Ž0.81.
Log-likelihood value y2463.45
y0.16 ) ) Žy3.09.
0.17 ) ) Ž8.75.
y0.02 Žy1.00.
0.3Ey3 Ž1.00.
0.11) ) Ž2.34.
y0.6Ey3 Žy0.30.
y0.23 ) Žy1.86.
0.01 Ž0.22.
y2.32 ) ) Žy47.28.
y2436.07
y0.09 ) Žy1.65.
0.16 ) ) Ž8.00.
y0.02 Žy0.93.
0.3Ey3 Ž1.00.
0.10 ) ) Ž0.05.
y0.2Ey2 Žy0.75.
y0.31) ) Žy2.36.
0.13 ) ) Ž4.41.
y1.54 ) ) Žy2.92.
y2195.87
a
Corresponds to Eq. Ž7. in text.
Corresponds to Eq. Ž10. in text.
c
Corresponds to Eq. Ž13. in text.
)
Significant at 10%.
))
Significant at 5%.
b
154
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
Table 6
Secondary job hours equations – Coefficients from self-select model for moonlighters only Ž t-statistics
in parentheses.
PJ hours constraineda
PJ hours not constrainedb
Full model c
A. variables in constrained equation
SJWAGE
23.76 ) ) Ž1.96.
VIRTUAL Y
0.1Ey2 Ž0.45.
H1
0.12 Ž0.33.
—
—
—
3.23 Ž0.29.
0.3Ey3 Ž1.03.
y0.45 ) ) Žy3.59.
B. variables in unconstrained equation
SJWAGE
—
NONLABY
—
PJWAGE
—
29.97 ) ) Ž2.56.
0.5Ey2 ) Ž1.84.
y34.55 ) ) Žy5.00.
42.41) ) Ž2.69.
0.2Ey3 Ž0.44.
y14.93 Žy1.61.
C. variables in all models
YNGKIDS
y46.88 Žy1.48.
NUMKIDS
y2.57 Žy0.18.
AGE
y25.65 ) Žy1.93.
AGE2
0.31) Ž1.82.
YRSEDUC
y151.87 ) ) Žy4.11.
YRSEDUC2
5.45 ) ) Ž3.84.
SICK
y11.00 Žy0.12.
MARRY
y41.34 Žy1.09.
MILLS
y44.15 Žy1.28.
CONSTANT
1775.12 ) ) Ž4.01.
F-Statistic
3.71) )
y50.84 ) Žy1.65.
6.59 Ž0.47.
y2.09 Žy0.15.
0.07 Ž0.39.
y144.04 ) ) Žy4.04.
5.89 ) ) Ž4.34.
y4.64 Žy0.05.
y22.85 Žy0.62.
31.48 Ž0.88.
1274.39 ) ) Ž3.74.
6.26 ) )
y0.14 Žy0.01.
13.84 Ž1.22.
y13.91 Žy1.30.
0.22 Ž1.59.
y91.19 ) ) Žy3.13.
3.39 ) ) Ž3.06.
y36.99 Žy0.52.
2.81 Ž0.09.
39.23 Ž1.40.
1215.77 ) ) Ž4.57.
28.17 ) )
a
Corresponds to Eq. Ž7. in text.
Corresponds to Eq. Ž10. in text.
c
Corresponds to Eq. Ž13. in text.
)
Significant at 10%.
))
Significant at 5%.
b
contribute nothing and their observations do not contribute to the resulting
parameter estimates. This would reduce the sample to approximately ten percent of
its current size. In the moonlighting hours equation, most individuals have only
one or two observations, again making fixed effects estimation infeasible 15 .
15
To explore how much the use of panel data is influencing our results, we also estimate the model
using the single cross-section that contains the highest number of moonlighters. Doing so results in a
sample 1r9th the size of the panel and that contains only 72 moonlighting observations. Estimating the
model with this greatly reduced sample has, for the most part, predictable effects on the results. In
particular, the estimated standard errors increase, often by enough to render the coefficient statistically
insignificant, but the signs and general magnitudes of most of the key coefficients remain unchanged.
The one exception is the full model estimated for moonlighting hours, in which the key estimated
parameters are all essentially zero. Note that this is the model with the smallest degrees of freedom and
the largest number of predicted variables so this result is not surprising.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
155
5.1. Results from the primary job hours equation
Table 4 contains the single equation estimates of primary job hours, a specification that assumes implicitly labor supply constraints do not exist in a meaningful
way, as well as the switching regression estimates. The single equation specification suggests that the wage elasticity is positive and statistically significant, but
small in magnitude Žapproximately q0.11.. In accordance with leisure being a
normal good, the non-labor income coefficient is negative and significant. In
general, the results are consistent with other work ŽKillingsworth, 1983; Pencavel,
1986., although our wage elasticity is at the positive end of the spectrum. Other
single equation studies using SIPP data also find wage elasticities at the high end
of the typical range ŽKimmel and Kniesner, in preparation.. The single equation
results, with a negative and statistically significant coefficient on the SJ wage, lend
support to the heterogeneous jobs motive. The remaining variables are roughly
consistent with a priori expectations; therefore, we have a reasonable benchmark
with which to compare our results.
Turning to the switching regression labor supply estimates, we find that the
wage elasticity increases a great deal in magnitude, from q0.11 in the single
equation model to q1.07 in the switching regression labor supply model. Such an
increase makes intuitive sense. If we ignore the fact that a substantial number of
individuals are unable to adjust their labor supply on their primary jobs, then labor
supply will appear less responsive to wage changes. When we allow for labor
supply constraints as an additional explanation for observed labor supply, we find
that desired labor supply is much more responsive to the wage. This contrasts with
other studies that use survey information about labor supply constraints, such as
Kahn and Lang Ž1991. and to a lesser extent Ham Ž1982., which tend to find a
small upward bias in the wage coefficient if labor supply constraints are ignored.
Douglas et al. Ž1995. provide evidence that this upward bias may be caused by
using ‘noisy’ survey information to detect labor supply constraints. Thus, our
results may differ because we do not use survey information to identify constrained workers or because of the shorter time frame of our data.
Some variables other than the primary job wage become less important in this
setting. In particular, non-labor income, although still negative, is no longer
statistically significant. The education variables are also no longer important
factors. A possible explanation is that these variables are more closely associated
with the likelihood that a worker will face an hours constraint on his primary job
than as a determinant of desired labor supply behavior. Ham Ž1982. comes to a
similar conclusion, finding that the effects of education on desired labor supply are
diminished when labor supply constraints are incorporated explicitly.
The estimated labor constraint equation is reported in the last column of Table
4. At first glance, it is somewhat startling to find a positive wage coefficient.
However, the results are actually quite intuitive, given that this is not a true labor
demand equation, but rather one that describes the upper bound on hours worked
156
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
faced by a given worker on his primary job. In general, higher paid workers are
likely to have jobs that require or at least permit longer hours. Likewise, a lower
unemployment rate, an indicator of local economic conditions, leads to greater
hours permitted on the primary job. Specific characteristics of the worker also
prove important. Non-white workers face greater labor supply constraints Ža lower
H1 . and more educated workers face fewer constraints 16 . Both of these results are
consistent with the findings of Ham Ž1982.. Finally, results for the region,
occupation and industry controls are not reported due to space considerations but
are available upon request.
The covariance estimates of the errors also tell an interesting story. The
variance of the labor demand equation is much smaller than that of the labor
supply equation, suggesting that desired labor supply is more likely determined by
unobserved factors such as tastes and ability. The correlation between the labor
supply and labor demand disturbances, r , is positive, but not statistically significant. A positive r suggests that labor supply constraints may be a short-run
phenomena as workers with high desired labor supply find jobs with high upper
limits on hours worked.
With the estimated labor supply and labor demand parameters and Žco.variances, we estimate the probability that a worker is constrained, conditional on his
observed number of hours. We find that labor supply constraints are extremely
important; approximately 83.9% of the sample has a conditional probability of
being constrained exceeding 0.9. Nine percent have a probability between 0.8 and
0.9, and, at the other extreme, only three percent of the sample have a probability
of less than 0.1. Surprisingly, moonlighters appear to face relatively fewer
constraints than non-moonlighters 17 . Thus, although our results point to labor
supply constraints on the primary job, they do not completely resolve the question
of why people choose to moonlight.
As mentioned earlier, the disequilibrium approach has shortcomings. We
estimated several different permutations from our basic switching regression
model to assess the sensitivity of our chosen specification 18 . These permutations
included: Ži. adding a race dummy to the labor supply equation; Žii. excluding the
SJ wage from the labor supply equation; Žiii. replacing time and time-squared with
time dummies in the labor demand equation; and Živ. two alternatives using
logged values Žsemi-logged and double-logged.. Most of these switching models
converged and produced results Žcoefficients as well as predicted probabilities of
being constrained. that are quite similar to the results presented in this paper. The
version with the time dummies had convergence trouble, but the nearly-converged
16
Specifically, the quadratic in education reaches its minimum at approximately 10 years of
education. This implies that each year of education beyond 10 years increases the upper bound, H1 ,
imposed on the primary job.
17
For instance, only 55% have a probability over 0.9 and 25% have a probability less than 0.1.
18
We thank the journal referees for suggesting most of these permutations.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
157
results were robust and also quite similar to the basic model. The logged versions
encountered convergence trouble. The version using the natural logarithm of the
dependent variables with no logs on the right hand side of the regression did not
converge at all. However, the double log version did converge and had results
similar to the basic findings. The convergence difficulties are not too surprising
given the overall sensitivity of switching regression models. There is no theoretical
reason for this problem, but it is reassuring that the non-converged results are
robust and similar to the results in Table 4.
In sum, our primary job hours equation estimates suggest that allowing
observed hours to deviate from desired hours significantly alters the estimated
desired labor supply equation. In particular, labor supply is more responsive to
wage changes than what is typically suggested by equilibrium models. This result
is consistent with the very high estimated probabilities of being constrained for
most workers and suggests that moonlighting may be the only avenue for short
term labor supply adjustments. However, we also find that the predicted wage on
the secondary job affects desired labor supply on the primary job and that
moonlighters have lower estimated probabilities of being constrained than other
workers. Both of these results suggest that the heterogeneous jobs motive is
present also.
5.2. Results for the moonlighting equation
We estimate the moonlighting equation two ways. Table 5 reports the results of
a probit moonlighting participation equation estimated for all workers, and Table 6
reports the results from a second job hours regression estimated for moonlighters
only, correcting for self-selection bias 19 . The first column of both tables lists the
estimates from the specification that assumes that the only motive for moonlighting is as a response to primary job constraints Ž hc2 written in Eq. Ž7... The second
column lists the estimates resulting from the heterogeneous jobs motive Žor hu2
written in Eq. Ž10... The last column reports results from the full model that
allows both motives Žwritten in Eq. Ž13...
Focusing first on the moonlighting participation results, we find strong support
for the constraint motive ŽTable 5, column 1.. The coefficient on H1 is statistically
significant and negative, as the theoretical model developed earlier suggests.
Likewise, the coefficient on virtual income is negative and statistically significant,
consistent with leisure being a normal good. The wage coefficient is positive, but
not quite statistically significant. The heterogeneous jobs motive also finds support
19
We also estimated the model with a tobit hours equation for all workers, yielding results that
perfectly mimicked those of the probit model. Given the large proportion of non-moonlighters, one
would expect the participation decision to dominate the hours supplied decision in a tobit model, so this
result is not surprising.
158
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
in Table 5 Žcolumn 2.. Both the SJ wage and non-labor income coefficients are
now statistically significant and of the expected sign. More importantly, the wage
coefficient on the primary job is negative and statistically significant, which is
consistent with the heterogeneous jobs motive where the labor supplied to the PJ
and to the SJ are not necessarily perfect substitutes.
The full model includes both motives and provides some support for both. In
general, the coefficients of interest are of the expected sign and some are
statistically significant. These results are especially striking given the very high
estimated probabilities of being constrained that are used in estimating this model.
Table 5 suggests that wage effects are stronger in the unconstrained than in the
constrained moonlighting equation. It makes sense that workers who are voluntarily allocating their labor supply between two heterogeneous jobs will be more
responsive to wage changes than workers who are forced into considering a
second job due to labor supply constraints on their first job. The limit placed on
hours worked on the PJ Ž H1 ., is the most statistically significant economic
variable in the constrained decision when both motives are allowed.
The continuous hours equation, reported in Table 6, also provides support for
the full model. Permitting both motives for moonlighting appears important as the
overall significance of the model Žmeasured by the F-statistic. increases a great
deal when both motives are considered, and the results of each model are affected.
Also, the parameter estimates easily satisfy the restriction that both hc2 and hu2 are
greater than or equal to zero 20 . In general, the full model provides estimates that
are similar to those in the participation equation in that the unconstrained
moonlighting equation is much more wage responsive than the constrained one
and H1 is the most statistically significant economic determinant of constrained
moonlighting behavior. However, non-labor income does not appear to be important to moonlighting hours whereas it is consistently important to the decision to
moonlight. In sum, the results from Tables 5 and 6 strongly suggest that both
motives are present in both the decision to take a second job and the choice of
how many SJ hours to supply 21 .
We test the constrained model versus the unconstrained model, and the
superiority of the full model over the other two with the test for overlapping
models developed by Vuong Ž1989.. These models are overlapping because they
share the vector of taste variables Že.g., age and education. but they are not nested.
In essence, Vuong’s test involves calculating the usual likelihood ratio between the
two competing models for each observation and then the variance of this likeli20
See 10 . Specifically, we predict the constrained and unconstrained moonlighting hours for all
moonlighters and find that all predictions are positive.
21
We re-estimated the full model using 0 or 1 in place of the predicted probability of being
constrained, based on whether the actual prediction is greater or less than 0.5. This version produced
nearly identical results to our basic model. This was to be expected given the distribution of our
predicted probabilities.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
159
hood ratio across all observations, and finally constructing an asymptotically
standard normal statistic. The null hypothesis is the equality of the two models,
which can be rejected in favor of one model or the other, depending on the sign of
the statistic. The full model dominates both of the other two, and the constrained
model is rejected in favor of the unconstrained model 22 .
Another implicit test of labor supply constraints on the primary job is to
perform an exogeneity test on all variables that are functions of primary hours
Ž H1 .. Recall that there are two possible measures for H1 , observed primary job
hours and the upper bound predicted from the labor demand equation. By
estimating the models using both measures of H1 Žand virtual income, which is a
function of H1 ., we test whether observed primary job hours are exogenous. For
both full models Žcolumn 3., we reject exogeneity at 10% significance or higher.
For the constraint motive-only models Žcolumn 1., we fail to reject exogeneity 23 .
This suggests that including primary hours as a regressor in a moonlighting
equation, as most researchers do, is not a sound practice and may lead to biased
parameter estimates.
It is difficult to compare our results directly to the literature because our data
and methods greatly differ and no general consensus presently exists. Our SJ wage
elasticities, which range from 0.04 to 0.47, are at the low end of the ranges
reported by Shishko and Rostker Ž1976. and Krishnan Ž1990.. The elasticities
reported by O’Connell Ž1979. 24 are at the high end, and Lilja Ž1991., who uses
Finnish data, is alone in obtaining negative elasticities of y0.142 to y0.09. All
studies that include the PJ wage, including ours, find that it has a negative effect.
Given that the two wages tend to be positively correlated, omitting the PJ wage
from the moonlighting hours equation as Lilja Ž1991. and Krishnan Ž1990. do will
likely bias the SJ wage coefficient downward; this may explain Lilja’s negative
elasticities. Our estimated coefficient on H1 in the full model is closer to the
expected value of y1.0 than Shishko and Rostker Ž1976. or Krishnan Ž1990..
O’Connell Ž1979. is alone in estimating a coefficient that exceeds 1.0, and Lilja
Ž1991. fails to include the variable. In general, then, our results are fairly close to
22
The specific statistics for the probit equations are y2.85 and y10.48 for the constrained against
the unconstrained and the full models respectively, and y9.88 for the unconstrained against the full
model. For the self-select hours equation, the corresponding statistics are y2.54, y7.64 and y7.39.
23
We perform a Hausman exogeneity test ŽHausman, 1978. by testing the equality of the virtual
income and PJ constraint coefficients when observed PJ hours versus our predicted measure of H1 is
used. Specifically, the test statistic is TqV
ˆ Ž qˆ . -1 q,
ˆ where qˆ is the difference between the estimated
coefficients when observed PJ hours are included and when our predicted value is used, and V Ž qˆ . is the
covariance matrix of q,
ˆ which Hausman shows is equal to the difference in the covariance matrices of
the two subvectors of coefficients. Calculations for the probit estimates of the constraint-only and full
models yielded Chi-squared statistics of 0.09 and 5.67, respectively. The self-select hours equations
yielded Chi-squared statistics of 3.83 and 16.90, respectively.
24
The secondary wage elasticity reported by O’Connell Ž1979. in Table 1, p. 75 holds the marginal
tax Ž t ) w 2 . constant and requires adjustment in order to be comparable.
160
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
Table 7
Sensitivity of primary job hours equations to different treatments of moonlighters
1. omit moonlighters, controlling for self-selection
2. include moonlighters, use imputed wage
Žtotal earnings r total hours.
h1 q h 2 s b ŽŽ w1 h1 q w 2 h 2 .rŽ h1 q h 2 ..q d Y
3. include moonlighters, treat as unconstrained
h1 s b w 1 q d Y
4. include moonlighters, treat as constrained
h1 s b w1 q d Y if not moonlighting,
h1 q h 2 s b w 2 q d wŽ w1 y w 2 . h1 qY x if moonlighting
Wage coefficient
Ž t-statistic.
Non-labor income
coefficient
4.83 ) ) Ž5.91.
13.88 ) ) Ž20.1.
y0.001) ) Žy4.84.
y0.001) ) Žy4.8.
7.96 ) ) Ž10.93.
y0.001) ) Žy4.60.
y5.79 ) ) Žy9.57.
y0.00016 Žy0.6.
what others have found, but they emphasize the importance of including the PJ
wage.
What, then, do our first stage and second stage results tell us about primary
labor supply and moonlighting behavior? Our switching regression model of
primary job hours suggests that constraints on hours worked are widespread, and
that failing to take account of these constraints may erroneously make desired
male labor supply appear less wage-responsive. However prevalent labor supply
constraints may be, our exogeneity tests reveal that treating observed primary job
hours as exogenous is inappropriate and may lead to biased parameter estimates in
the moonlighting equation. Furthermore, we find strong support for a theoretical
model that permits workers to moonlight in response to either constraints on their
primary jobs or nonpecuniary Žor unobserved. differences between their two
jobs 25 .
5.3. How important are moonlighters to primary job labor supply estimates?
Of primary importance to most labor economists, however, is the estimated
labor supply elasticity on the primary job. Given that moonlighters make up such a
small proportion of the population, how important are they to PJ labor supply
estimates? And what is the best way for a researcher to deal with moonlighters
when moonlighting behavior, per se, is not the focal point of the study? To explore
this issue we estimate a typical PJ labor supply equation Žsingle equation with no
SJ wage., treating moonlighters in a number of ways, such as omitting them from
the sample or treating them as constrained and using the marginal wage and virtual
25
Our results are consistent with those of Paxson and Sicherman Ž1996. who use the PSID and
include self-reported labor supply constraints as a determinant of the decision to take a second job.
They find that labor supply constraints help explain some, but not all, types of moonlighting behavior.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
161
income. These estimates are presented in Table 7 for the wage and non-labor
income coefficients only.
A very consistent story emerges from this table. Moonlighters tend to be more
wage-responsive than non-moonlighters Žthis is confirmed by estimating a PJ
equation for moonlighters only., so omitting them from the sample tends to bias
the wage coefficient downward. However, given their relatively small size, this
bias is not large. In fact, it appears that the most serious mistake a researcher can
make is to treat all moonlighters as if they are constrained on their PJ. This results
in a negative wage coefficient and a zero non-labor income coefficient, producing
a theoretically-inconsistent negative compensated wage effect 26 . The most prudent strategy may therefore be to omit moonlighters from the sample, recognizing
that in so doing one may have dropped the most wage-responsive individuals. This
strategy is likely preferable to one that arbitrarily assigns one motive or another
for moonlighting behavior.
6. Concluding remarks
We build on the theoretical and empirical literature on male labor supply
behavior by exploring more carefully an avenue for labor supply adjustment that is
typically ignored, the ability to take a second job. We consider two motives for
moonlighting, as a response to primary job constraints or differential non-wage
benefits and costs. Modeling primary job and secondary job hours equations that
are consistent with these two motives provides tests of these competing theories of
moonlighting and helps determine whether labor supply constraints exist on the
primary jobs of most workers. For the most part, our empirical results are
consistent with theory. The results point to the conclusion that a significant
number of workers are constrained on their primary jobs and therefore constraints
play an important role in moonlighting behavior. However, treating all workers as
if they are constrained, as most studies do, is rejected soundly by the model.
Furthermore, the data support the hypothesis that people may also moonlight
because jobs are heterogeneous. Perhaps most importantly, we find that once labor
supply constraints on the primary job have been modeled appropriately and more
than one motive for moonlighting is permitted, desired male labor supply is quite
responsive to wage changes. Failing to consider the option of moonlighting and
the possibility of facing labor supply constraints appears to bias male wage
elasticities downwards.
Our research has important implications for labor supply research. It emphasizes the need to better incorporate demand-side factors into studies of obserÕed
26
The results are the same when the PJ is defined as the job with the greatest number of hours rather
than the highest wage.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
162
labor supply on the primary job. We also find that the typical methods of treating
moonlighters Ždropping them from the sample, ignoring their labor supply on the
second job, or aggregating hours on all jobs. are inadequate. However, there is
still much to be done in this line of research. While we believe that our data are
the best available, the SIPP is not ideal due to the inability to incorporate taxes and
the small number of moonlighters. A larger sample might yield a less sensitive
switching model, although our findings appear to be robust. Furthermore, our
theoretical model is a static one in which intertemporal decision making has been
ignored. In a life-cycle framework, if a worker faces temporary labor supply
constraints on his primary job, he may choose to moonlight or plan to work more
in the future when the constraints will be removed. Future efforts in this area
might also attempt to control for unobserved individual heterogeneity, although the
data requirements for such a contribution will likely be quite difficult to satisfy.
Nonetheless, the theoretical model and empirical results presented here have
important ramifications for the manner in which most labor supply research treats
moonlighters and the possibility that workers may face labor supply constraints.
Acknowledgements
The authors, whose names are listed alphabetically, wish to thank Strat
Douglas, Marvin Karson, Stanley Sedo, Jim Ziliak, and participants in our session
at the 1992 Winter Meeting of the Econometric Society for their comments,
Rebecca Jacobs for her superb research assistance, and Claire Black for her
secretarial support. This paper also benefits from the careful suggestions of two
anonymous referees. An earlier draft appeared as W.E. Upjohn Institute Working
Paper a92-09, Moonlighting Behavior: Theory and Evidence, June 1992.
Appendix A. Technical appendix
In order to derive a reduced form moonlighting participation equation for the
initial stage, begin with the structural participation equation,
H2 s H2c Ž w 2 , Y q Ž w 1 y w 2 . H1 , H1 . )Pr Ž h1s ) h1d .
q H2u Ž w1 , w 2 , Y . ) Ž 1 y Pr Ž h1s ) h1d . . ,
Ž A.1 .
based on Eq. Ž13. in the text. Variables in Eq. ŽA.1. that are endogenous or
unobserved are w1 , w 2 , H1 and PrŽ h1s ) h1d .. We derive the reduced form equation
by substituting in for these variables.
The wage equations are written in Fig. 3 and can be rewritten here as
wi s X wbiw ,
where X
w
Ž A.2 .
2
2
contains age, age , education, education , age)education, plus all of
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
163
the exogenous variables in X d , which are listed in Table 4. H1 is the upper bound
on primary job hours and is written in Fig. 3 as
H1 s X db d .
Ž A.3 .
d
However, X includes w 1 , so substituting in for w 1 into Eq. ŽA.3. implies that H1
is also a function of all variables in the wage equation, or
H1 s X wP d .
Ž A.4 .
PrŽ h1s ) h1d ..
This leaves only
Based on our model, the probability that
s s
Pr Ž h1s ) h1d . s Pr Ž ´ d y ´ s - X sb s y X db d . s F
ž
h1s ) h1d
is
d d
X b yX b
s̃
/
Ž A.5 .
where F is the cumulative normal distribution function and s̃
s ss 2 q sd2 y 2 rss sd . As is well known, F Ž. has no closed form solution, so
we use the logistic distribution as an approximation,
(
Pr Ž
h1s ) h1d
e Xb
X
. , 1 q e Xb
Ž A.6 .
X
where X s Ž X s , yX d . and b X s Ž b s , b d .. Recognizing that both X s and yX d
contain one or both wages implies that Eq. ŽA.6. be rewritten as
Pr Ž
h1s ) h1d
eX
all
b all
Ž A.7 .
all all
1qe X b
where X all contains all of the variables in X w and all of the exogenous variables
in X s . Thus, X all contains all of the exogenous variables in the system. Using a
Taylor series linear approximation to Eq. ŽA.7. and expanding around zero yields
.,
Pr Ž h1s ) h1d . , 12 q 14 X allb all .
Ž A.8 .
all
Note that if b s 0 then the probability is 0.5, which a priori is a reasonable
baseline. However, because X all contains a constant term, the probability need not
be 0.5 even if all other X ’s Žor b ’s. are zero. Indeed, what our disequilibrium
model estimates show is that b all does not equal zero and the probability of being
constrained is much greater than 0.5 on average.
Substituting Eqs. ŽA.2., ŽA.4. and ŽA.8. into Eq. ŽA.1. produces
H2 s H2c Ž X wb 1w , Y q X w Ž b 2w y b 2w . P X wP d , X wP d . ) Ž 12 q 14 X allb all .
q H2u Ž X wb 1w , X wb 2w , Y . ) Ž 1 y 12 y 14 X allb all . .
w
all
w
Ž A.9 .
all
Recognizing that X is a subset of X , that both X and X
include a
constant and that H2j , j s c, u, is specified as linear greatly simplifies Eq. ŽA.9..
Collecting terms yields
H2 s Au 1 q Bu 2 ,
where A i is equal to
Yi m X iall
Ž A.10 .
and the i subscript denotes row i, ; i s 1, . . . , N.
164
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
Likewise, Bi is equal to X iall m Ci , where Ci is equal to X iw m X iw ; u 1 and u 2 are
the reduced form parameters. The final matrix B consists of all of the unique
elements of the Bi ’s and thus contains all of the squares, cubes and cross-products,
for each observation, of the matrices X w and X all.
However, given that X w has 28 variables and X all has 33 variables, Eq.
ŽA.10. includes hundreds of unique explanatory variables, making the estimation
infeasible. Even if we omit the large number of dummy variables, X w has eight
variables and X all has 10 variables, thereby yielding Bu with 640 variables 27 .
We therefore impose the following restrictions: Ž1. we set u 2 s 0, and Ž2. we
include the industry, occupation, and region dummies only linearly and do not
interact them with the other variables. These restrictions were imposed to reduce
both the large number of explanatory variables and the extremely high multi-collinearity. Even so, the restricted specification has 70 regressors. Because the
reduced form probit estimates are used only to construct an inverse Mills ratio to
be included in the second job wage and the moonlighting hours equations makes it
unlikely that these restrictions have much effect on the final estimates. In addition,
in earlier drafts of this research we specified the reduced form probit as a linear
function of X all ; changing to the above specification did not substantively affect
our results. Therefore, we do not expect that adding the additional regressors to
match the full version implied by Eq. ŽA.10. would alter the final results.
Appendix B. Data description
Each individual in the SIPP can report detailed employment information for up
to two jobs at each interview. Thus, many individuals possess two complete job
records at multiple waves. We distinguish actual moonlighters from those who
held two jobs within a wave but not simultaneously by using job start and end
dates. Reported weekly hours may be a problem for the small number of partial
job overlappers in our sample because it is not possible to assess if the individual
reports the usual hours for the duration of the overlap or for when there is no
overlap. Treating these partial overlappers as non-moonlighters does not substantively alter our empirical results. Another potential source of error is that persons
with brief periods of non-employment during a wave may have their weeks
employed overstated because of misreported or misleading job start and end dates
in the SIPP’s monthly records. Extensive data checks confirmed that the possibly
overstated hours of work Žand therefore understated imputed wages. for persons
briefly without jobs is of no empirical importance to our results 28 . Finally, fewer
27
While several of these 640 variables will not be unique because 7 of the continuous variables are
the age-education polynomial terms, time, and time-squared, there will still be a very large number of
variables.
28
We thank Theresa Devine for bringing this subtlety of the SIPP’s monthly records to our attention.
K. Smith Conway, J. Kimmelr Labour Economics 5 (1998) 135–166
165
than 6.6% of the moonlighting observations indicate having three or more
employers in one wave. This figure may be inflated because it may overstate the
number of jobs actually worked; e.g. someone who is on layoff may continue to
list that employer. Because the SIPP only collects data for two jobs, we are forced
to ignore any jobs beyond the first two. However, the fact that the respondent is
asked to provide information on their two most important jobs and that only a
small number of observations are affected make us confident that this omission is
not serious.
The hours of work information available in the SIPP includes the usual number
of hours worked per week and the reported number of weeks worked per wave on
each job. Because the number of weeks per wave varies from 17 to 18, we have
normalized it using 17.33 as the maximum number of weeks per wave. For
example, a person with 10 weeks employed in a 17-week wave would have a
normalized weeks worked variable of 10)Ž17.33r17., or 10.19. Hours of work
per wave was then created by multiplying the usual number of hours worked per
week by this normalized variable.
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